The cooler material between an aluminum plate and a tile depends on the context in which they are being compared. Generally, aluminum plates are cooler to the touch than tiles. This is because aluminum has a higher thermal conductivity than most tiles. Thermal conductivity measures how well a material can transfer heat. Aluminum has a thermal conductivity of approximately 237 W/m·K, while ceramic tiles, which are commonly used in construction, have a thermal conductivity of around 2.5 W/m·K. This significant difference means that aluminum can dissipate heat much more efficiently than tiles.

In a practical scenario, such as in the kitchen or bathroom, where heat is generated from appliances or sunlight, aluminum plates would cool down faster than tiles. For instance, if you place a hot pan on an aluminum plate, it will cool down more quickly compared to a ceramic tile. This is due to the aluminum's ability to conduct heat away from the source more effectively.

Data from the American Society for Testing and Materials (ASTM) and other material science research supports this claim. According to a study published in the Journal of Materials Science, the thermal conductivity of aluminum is 237 W/m·K, which is significantly higher than that of ceramic tiles. This study also highlights the importance of thermal conductivity in various applications, including heat sinks and thermal management systems.

In conclusion, based on thermal conductivity, aluminum plates are cooler than tiles. This is due to the higher thermal conductivity of aluminum, which allows it to dissipate heat more efficiently.